Given $ m \angle AOB = 3x - 2$, $ m \angle BOC = 8x + 23$, and $ m \angle AOC = 142$, find $m\angle AOB$. $O$ $A$ $C$ $B$
Explanation: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {3x - 2} + {8x + 23} = {142}$ Combine like terms: $ 11x + 21 = 142$ Subtract $21$ from both sides: $ 11x = 121$ Divide both sides by $11$ to find $x$ $ x = 11$ Substitute $11$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 3({11}) - 2$ Simplify: $ {m\angle AOB = 33 - 2}$ So ${m\angle AOB = 31}$.